Finite Group DatabasebetaFinite Group Databasebeta| order | 10201 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C25×C101 (order 10100) · Inn(G) = C1 · Out(G) = C4×C25×C101 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10201 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, socle, prime radical, cosocle | C101 | C101 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C101 ▷ C1 | |
3 conjugacy classes of subgroups.
10201 conjugacy classes. The character table is too large to display.
| derived subgroup of | D10201 |
| Fitting subgroup of | D10201 |
| maximal subgroup of | D10201, C2×C10201, C3×C10201 |
| maximal normal subgroup of | D10201, C2×C10201, C3×C10201 |
| maximal quotient of | C2×C10201, C3×C10201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10201, 1);